TEKS Focus:
 (6)(B) Prove two triangles are congruent
by applying the Side-Angle-Side, AngleSide-Angle, Side-Side-Side, AngleAngle-Side, and Hypotenuse-Leg
congruence conditions.
 (1)(G) Display, explain, or justify
mathematical ideas and arguments using
precise mathematical language in
written or oral communication.

Geometric figures are congruent if they are the
same size and shape.
Corresponding angles and corresponding sides
are in the same position in polygons with an
equal number of sides.
Two polygons are congruent polygons if and
only if their corresponding sides are congruent.
Thus triangles that are the same size and shape
are congruent.
CPCTC is an abbreviation for the
phrase “Corresponding Parts of
Congruent Triangles are Congruent.”
It can be used as a justification in a
proof after you have proven two
triangles congruent.
To name a polygon, write the vertices in
consecutive order. For example, you can name
polygon PQRS as QRSP or SRQP, but not as
PRQS.
In a congruence statement, the order of the
vertices indicates the corresponding parts.
P
Q
S
R
Some hikers come to a river in the woods. They
want to cross the river but decide to find out how
wide it is first. So they set up congruent right
triangles. The figure shows the river and the
triangles. Find the width of the river, GH. Explain.
5 meters, by using CPCTC
Example: 2
Use the diagram to prove the following.
STATEMENT
REASON
1. BA  DA
1. Given
2. CAB  EAD
2. Vertical Angle Theorem
3. CA  EA
3. Given
4. BAC  DAE
4. SAS
5. C E
5. CPCTC
Example 3:
STATEMENT
REASON
1. AB  AC
1. Given
2. M is the midpoint of BC
2. Given
2. BM  MC
2. Definition of Midpoint
3. AM  AM
3. Reflexive Prop. of Congruence
4. AMB  AMC
4. SSS
5. AMB  AMC
5. CPCTC
Example 4:
STATEMENT
REASON
1. KN and LM bisect each other
1. Given
2. KH  HN and LH  HM
2. Definition of Segment Bisector
3. KHL   NHM
3. Vertical Angle Theorem
4. KHL  NHM
4. SAS
5. KLH  NMH
5. CPCTC
6. KL || MN
6. Converse of Alternate Interior
Angles Theorem